Summary
Gas and water coning significantly reduce oil production, while increasing
production costs. Simulation and experimental methods, coupled with simple
analytical solutions or correlations, are typically used to identify the oil
rate that minimizes coning and maximizes recovery. Current analytical
solutions, however, are overly simplified in that they assume negligible
capillary pressure, which leads to segregated flow. This paper presents new
benchmark analytical solutions that relax this assumption and also allow for
simultaneous two-phase flow.
The new coning solutions apply to vertical wells where in-situ fluids are in
vertical equilibrium. The development identifies the important dimensionless
groups that control the effect of coning on oil recovery and illustrates how
simultaneous two-phase flow affects capillary fluid levels in the formation.
Dimensionless two-phase production windows are constructed to identify critical
rates, the largest oil rate at which water (or gas) will not be
produced. From comparisons to simulation, we show that critical flow rate
estimates are accurate for aspect ratios greater than approximately
10. For aspect ratios less than 10, the critical rate estimates are always
conservative.
Introduction
Water and gas coning are serious problems in oil production. A large oil
rate may cause a second fluid to be produced through upward coning of water or
downward coning of gas into the well perforations. Once the second fluid is
produced, the oil rate is significantly reduced and the cost of water and gas
handling is increased.
It is a common industry practice to reduce water coning in oil reservoirs by
perforating vertical wells as far above the oil/water contact (OWC) as possible
and to produce the wells at or below the critical oil rate. Similarly, wells
are often perforated low in the oil column away from the gas/oil contact (GOC)
in gas/oil reservoirs. The benefits of this practice are mixed in that limited
perforations may increase the pressure gradient (the drawdown) near the well,
which can exacerbate coning.
There has also been success in reducing coning with polymers and gels.1 A
more recent and novel approach is to use downhole water-sink technology (DWS)
where water is produced separately from the oil using dual packers.2 The water
production below the OWC may reduce upward water coning so that the oil rate
can be increased. The DWS technology, however, requires a good understanding of
how fluid rates affect coning.
Dupuit3 published one of the first papers on the down coning of air into
aquifers. The Dupuit equation, which assumes vertical equilibrium, gives the
steady-state relationship between the water production rate and water table
elevation in the vicinity of a wellbore. The flowing water is segregated from
the static air phase because capillary pressure is assumed to be negligible.
The Dupuit equation is still used today to determine the elevation of the water
table when water is produced to a pumping well.4,5
Muskat and Wyckoff,6 who coined the term “water-coning,” derived an
approximate steady-state solution for 2D water coning in an oil reservoir. The
water is assumed to be stationary at steady-state oil flow so that water
production is not allowed. Pirson7 extended the Dupuit approach to single-phase
flow of oil in a gas/oil/water reservoir. All of the more recent methods
have assumed segregated flow or have used numerical simulation.8–12
Relaxing the assumption of segregated flow in an analytical model is a goal of
this work.
The research reported in this paper derives new solutions of “Dupuit form”
that allow for both single- and simultaneous two-phase flow that include the
effect of capillary pressure and relative permeability on fluid interfaces. The
first section presents the mathematical model, the assumptions used, and the
derivation of the general integral equation. The next sections present
solutions of this equation for both single-phase flow and for simultaneous
two-phase production of gas or water. We then discuss and illustrate the
effects of flow rates and scaling groups, such as the Bond number, on the fluid
interfaces. Last, we compare the analytical results to numerical simulation to
determine when the analytical solutions are most valid. The new exact
solutions are useful because they (a) provide benchmark solutions for
validation of numerical simulation, (b) are significantly faster to estimate
critical flow rates than with numerical simulation, (c) identify important
scaling groups, and (d) aid in the development of DWS completion
technology.1
© 2005. Society of Petroleum Engineers
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History
- Original manuscript received:
21 January 2003
- Revised manuscript received:
10 June 2005
- Manuscript approved:
8 July 2005
- Version of record:
15 December 2005
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